p11_003.pdf

3. (a) The time for one revolution is the circumference of the orbit divided by the speed v of the Sun:

T =2 πR/v ,where R is the radius of the orbit. We convert the radius:

R = 2 . 3

10 4 ly 9 . 46

10 12 km / ly =2 . 18

10 17 km

km conversion can be found in Appendix D or ﬁgured “from basics” (knowing the

speed of light). Therefore, we obtain

T = 2 π 2 . 18

↔

10 17 km

250 km / s

=5 . 5

10 15 s .

(b) The number of revolutions N is the total time t divided by the time T for one revolution; that is,

N = t/T . We convert the total time from years to seconds and obtain

N = 4 . 5

10 9 y 3 . 16

10 7 s / y

=26 .

5 . 5

10 15 s

where the ly